Robust Score Testing in GLMs, by Sign-Flip Contributions

It provides robust tests for testing in GLMs, by sign-flipping score contributions. The tests are often robust against overdispersion, heteroscedasticity and, in some cases, ignored nuisance variables.

Author

Livio Finos, Jelle Goeman and Jesse Hemerik, with contribution of Riccardo De Santis.

Examples

set.seed(1)
dt=data.frame(X=rnorm(20),
   Z=factor(rep(LETTERS[1:3],length.out=20)))
dt$Y=rpois(n=20,lambda=exp(dt$X))
mod=flipscores(Y~Z+X,data=dt,family="poisson",x=TRUE)
summary(mod)
#> 
#> Call:
#> flipscores(formula = Y ~ Z + X, family = "poisson", data = dt, 
#>     x = TRUE)
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -1.6910  -0.5792   0.1012   0.4900   1.0440  
#> 
#> Coefficients:
#>             Estimate   Score Std. Error z value Part. Cor Pr(>|z|)   
#> (Intercept)  -0.1026 -0.7229     2.7127 -0.2665    -0.088   0.7414   
#> ZB           -0.1501 -0.7125     2.1789 -0.3270    -0.104   0.6410   
#> ZC            0.1633  0.8106     2.2232  0.3646     0.117   0.6954   
#> X             0.9439 16.2062     4.7272  3.4283     0.671   0.0096 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for poisson family taken to be 1)
#> 
#>     Null deviance: 27.135  on 19  degrees of freedom
#> Residual deviance: 12.888  on 16  degrees of freedom
#> AIC: 57.459
#> 
#> Number of Fisher Scoring iterations: 5
#> 

# Anova test
anova(mod)
#> Analysis of Deviance Table (Type III test)
#> 
#> Model: poisson, link: log
#> 
#> Inference is provided by FlipScores approach (5000 sign flips).
#> 
#> Model: Y ~ Z + X
#>   Df   Score Pr(>Score)   
#> Z  2 0.75512     0.6960   
#> X  1 0.02990     0.0096 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# or
mod0=flipscores(Y~Z,data=dt,family="poisson",x=TRUE)
anova(mod0,mod)
#> Analysis of Deviance Table (Type III test)
#> 
#> Model: poisson, link: log
#> 
#> Inference is provided by FlipScores approach (5000 sign flips).
#> 
#> Model 1: Y ~ Z
#> Model 2: Y ~ Z + X
#>                    Df    Score Pr(>Score)  
#> Model 2 vs Model 1  1 0.029472     0.0112 *
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# and
mod0=flipscores(Y~X,data=dt,family="poisson")
anova(mod0,mod)
#> Error in model.frame.default(formula = Y ~ X, data = dt, drop.unused.levels = TRUE): 'data' must be a data.frame, environment, or list